Scala analysis: xen09-wilson-marwa-11a-05
Marwa permutation 5 from Figure 11a, Hawkins 16/15 135/128 32/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 32/27 294.134997 Pythagorean minor third 2: 512/405 405.866283 narrow diminished fourth 3: 4/3 498.044999 perfect fourth 4: 128/81 792.179997 Pythagorean minor sixth 5: 16/9 996.089998 Pythagorean minor seventh 6: 256/135 1107.821284 octave - major chroma 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 135/128 92.1787 major chroma, major limma 1: 32/27 294.1350 Pythagorean minor third 2: 16/15 111.7313 minor diatonic semitone 3: 135/128 92.1787 major chroma, major limma 4: 32/27 294.1350 Pythagorean minor third 5: 9/8 203.9100 major whole tone 6: 16/15 111.7313 minor diatonic semitone 7: 135/128 92.1787 major chroma, major limma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 135/128 92.179 cents major chroma, major limma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 32/27 294.135 cents Pythagorean minor third 2: 2 9/8 203.910 cents major whole tone 2: 1 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 1 512/405 405.866 cents narrow diminished fourth 2: 1 4/3 498.045 cents perfect fourth 3: 1 81/64 407.820 cents Pythagorean major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 45/32 590.224 cents diatonic tritone 3: 1 64/45 609.776 cents 2nd tritone 4: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 3/2 701.955 cents perfect fifth 5: 1 405/256 794.134 cents wide augmented fifth 5: 2 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/16 905.865 cents Pythagorean major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 15/8 1088.269 cents classic major seventh 6: 2 256/135 1107.821 cents octave - major chroma Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 294.1 405.9 498.0 792.2 996.1 1107.8 1200.0 294.1 : 111.7 203.9 498.0 702.0 813.7 905.9 1200.0 405.9 : 92.2 386.3 590.2 702.0 794.1 1088.3 1200.0 498.0 : 294.1 498.0 609.8 702.0 996.1 1107.8 1200.0 792.2 : 203.9 315.6 407.8 702.0 813.7 905.9 1200.0 996.1 : 111.7 203.9 498.0 609.8 702.0 996.1 1200.0 1107.8: 92.2 386.3 498.0 590.2 884.4 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 294.1350 cents 4096/3645, 201.9563 cents 135/128, 92.1787 cents 2: 203.9100 .. 498.0450 cents 32/27, 294.1350 cents 243/256,-90.2250 cents 3: 407.8200 .. 609.7763 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents 4: 590.2237 .. 792.1800 cents 4096/3645, 201.9563 cents 2025/2048,-19.5526 cents 5: 701.9550 .. 996.0900 cents 32/27, 294.1350 cents 243/256,-90.2250 cents 6: 905.8650 .. 1107.8213 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 135/128, 92.1787 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 1.859741 Largest / Average step : 1.715787 Largest / Smallest step : 3.190921 Median interval of one step : 16/15, 111.7313 cents, amount: 2 Least squares average step : 184.25786 cents, oct.: 1289.80501 cents Scale is not proper Step pattern alph. order: ABCADBC Step pattern size order : DBADCBA Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.389648 Lumma stability : 0.153631 Lumma impropriety factor : 0.317044 Rothenberg efficiency : 0.540136 redundancy: 0.459864 Efficiency x scale size : 3.780952 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 32805/32768, 1.9537 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Phrygian octave species of abstract tetrachord Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 5 Odd number limit : 405 (O: 405 U: 405) Highest odd numerator or denominator: 405 Scale harmonicity : 0.038363 Average absolute harmonicity : 0.219708 Specific harmonicity : 0.189648 Fundamental : 1/405, -8.6618 octaves, 0.6460 Hz. Guide tone : 512, 9.0000 octaves, 133952.289 Hz. Exponens Consonantiae : 2.073600E+05, 17.66178 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 805.5, average 115.07143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.50900, average 1.35843 Sum of Tenney's harmonic distance : 20.34608, average 2.90658 Vogel's harmonic complexity : 13.42857 Wille's k value : 202 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 129.53504, average 4.62625 Lattice compactness (without 2's) : 59.44782, average 2.12314 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 9 5.14286 36 1 3: -4 .. 0 -2.42857 17 4 5: -1 .. 0 -0.28571 2 2 Average exponent except 2's :-19 / 7 =-2.71429 Average absolute exponent except 2's: 19 / 7 = 2.71429 Scale is weakly epimorphic with val: <7 11 15| Scale is weakly epimorphic with val: <7 12 17|
FIT/MODE
7: 1 1 0 2 1 1 1 N T3 SD: 106.9259 c. M: 155.1879 c. 8: 2 0 1 2 1 1 1 N D3 SD: 63.1394 c. M: 105.8663 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 33.2253 c. M: 62.7567 c. 11: 3 1 1 2 2 1 1 N D3 S SD: 28.2345 c. M:-47.4095 c. 12: 3 1 1 3 2 1 1 N SD: 5.4804 c. M: 7.8213 c. Chromatic Phrygian 41: 10 4 3 10 7 4 3 N SD: 2.4287 c. M:-4.3738 c. 53: 13 5 4 13 9 5 4 N SD: 0.8917 c. M:-1.6809 c. 65: 16 6 5 16 11 6 5 N SD: 0.8705 c. M:-1.6662 c. 118: 29 11 9 29 20 11 9 N SD: 0.6856 c. M:-1.0403 c. 323: 79 30 25 79 55 30 25 N SD: 0.6181 c. M: 0.9127 c. 335: 82 31 26 82 57 31 26 N SD: 0.6147 c. M: 1.0902 c. 364: 89 34 28 89 62 34 28 N SD: 0.5242 c. M: 0.9712 c. 376: 92 35 29 92 64 35 29 N SD: 0.4365 c. M: 0.6906 c. 388: 95 36 30 95 66 36 30 N SD: 0.4166 c. M: 0.7116 c. 429: 105 40 33 105 73 40 33 N SD: 0.3169 c. M: 0.5716 c. 441: 108 41 34 108 75 41 34 N SD: 0.2713 c. M: 0.4241 c. 482: 118 45 37 118 82 45 37 N SD: 0.2498 c. M: 0.4788 c. 494: 121 46 38 121 84 46 38 N SD: 0.1690 c. M: 0.2772 c. 547: 134 51 42 134 93 51 42 N SD: 0.1170 c. M: 0.2239 c. 559: 137 52 43 137 95 52 43 N SD: 0.0771 c. M: 0.1418 c. 612: 150 57 47 150 104 57 47 N SD: 0.0158 c. M: 0.0231 c. 2395: 587 223 184 587 407 223 184 N SD: 0.0180 c. M: 0.0297 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 45.1125 cents 3 x x 4:5 x x 6 S SD: 30.7262 cents 4 x 5 x 6:7 x 8 S SD: 24.0653 cents 5:6 x 7:8:9 x 10 S SD: 18.4632 cents 6:7 x 8:9:11 x 12 SD: 21.6535 cents 7:8:9 x 11:12:13:14 SD: 16.8163 cents 9:11 x 12:14:16:17:18 SD: 10.0378 cents 10:12 x 13:16:18:19:20 SD: 9.6034 cents 12:14:15:16:19:21:23:24 SD: 6.7349 cents 15:18:19:20:24:27:28:30 S SD: 6.6121 cents 18:21:23:24:28:32:34:36 SD: 6.1855 cents 21:25:27:28:33:37:40:42 SD: 5.1657 cents 22:26:28:29:35:39:42:44 SD: 4.1566 cents 26:31:33:35:41:46:49:52 SD: 3.5763 cents 27:32:34:36:43:48:51:54 SD: 2.3619 cents 38:45:48:51:60:68:72:76 SD: 2.3294 cents 45:53:57:60:71:80:85:90 SD: 1.9297 cents 48:57:61:64:76:85:91:96 SD: 1.7558 cents 54:64:68:72:85:96:102:108 SD: 1.6766 cents 60:71:76:80:95:107:114:120 SD: 1.2015 cents 69:82:87:92:109:123:131:138 SD: 1.1913 cents 76:90:96:101:120:135:144:152 SD: 0.9333 cents 98:116:124:131:155:174:186:196 SD: 0.8587 cents 102:121:129:136:161:181:193:204 SD: 0.8009 cents 114:135:144:152:180:203:216:228 SD: 0.5751 cents 162:192:205:216:256:288:307:324 SD: 0.2902 cents 231:274:292:308:365:411:438:462 SD: 0.2871 cents 243:288:307:324:384:432:461:486 SD: 0.1935 cents 378:448:478:504:597:672:717:756 SD: 0.1691 cents 405:480:512:540:640:720:768:810 SD: 0.0000 cents